Recall the identity cos²x-sin²x = cos(2x).
Hello,
I'm having trouble with a trigonometry problem, outlined below:
cos²(2x) - sin²(2x) = (√3/2)
I'm not quire sure how to solve for x, can any of you help?
I would appreciate your assistance!
Thanks
I still don't quite understand the relationship between the identity you suggested:
cos²x - sin²x = cos(2x)
and the left term in the equation I have:
cos²(2x) - sin²(2x)
I'm not quite sure of what to do because of the '2x', otherwise I could easily substitute the identity you suggested.
EDIT:
I see now that in my case it would be cos(4x) as the substitution.
Okay, I didn't realize that other identity!
So I solved for x:
x = π/24
Just so I can understand how to solve more problems, how do you go about this? Do you have all the identities memorized? If I knew that cos(4x) = cos(π/6), then I could have solved this more easily.
I guess I should just memorize all the identities, is that the best way?
Right! That's what one solution, though. There are infinitely many. Can you find (or are you required to) find the rest?
No, cos(4x) = cos(π/6) is not an identity. Our equation was cos(4x) = (√3/2), but (√3/2) = cos(π/6) so we have cos(4x) = cos(π/6).Just so I can understand how to solve more problems, how do you go about this? Do you have all the identities memorized? If I knew that cos(4x) = cos(π/6), then I could have solved this more easily.
Memorisation will only get you so far; the best way is doing as many problems as you can get hold of.I guess I should just memorize all the identities, is that the best way?
A brilliant book is this one: Advanced Trigonometry - C. V. Durell and A. Robson. It's very old, so you can probably download it online for free too.